Spatial-temporal evolution of technology flows in China’s Beijing-Tianjin-Hebei region: Patent transfer networks 2003–2021

This paper presents new evidence on knowledge flows in the Beijing-Tianjin-Hebei region of China, involving 43 cities (districts) in the Beijing-Tianjin-Hebei region, based on the invention patent transfer data from the State Intellectual Property Office of China. First, the characteristics of technology flows in the Beijing-Tianjin-Hebei region are analyzed in terms of changes in the number of flows, types of flowing subjects and spatial distribution characteristics. Then, a multi-level patent technology flow network in the Beijing-Tianjin-Hebei region was constructed, and the structural characteristics and node characteristics of each level network were explored separately. The key findings of the study are as follows. (1) The number of patented technology flows has been growing over time, showing obvious phase characteristics during the study period. As a whole, the intra-city (district) technology flow in the Beijing-Tianjin-Hebei region is higher than the inter-city (district). (2) The multi-level patent technology flow network in the Beijing-Tianjin-Hebei region shows dynamic characteristics, with more and more mobile subjects participating in the patent technology flow network, some network nodes becoming closer to each other, and the trend of small group technology flow increasing significantly. (3) Enterprises are the core hub of the patent technology flow network in Beijing-Tianjin-Hebei region. Individual invention patent technology transfer also occupies a high proportion and the participation of universities and colleges in the patent technology flow network in the Beijing-Tianjin-Hebei region is gradually increasing. (4) Over time, the flow of patent technology in the 43 cities (districts) in the Beijing-Tianjin-Hebei region has gradually become active and no longer relies excessively on a particular city (district) for patent technology transfer.


Introduction
Innovation is the source of sustained growth in the world economy, and knowledge flow is one of the most essential and fundamental forms of achieving innovation [1].For regions, continuous innovation can only be accomplished through continuous knowledge flows with other regions.
In 2021, China's newly revised Law of the People's Republic of China on Scientific and Technological Progress once again emphasized the need to promote close cooperation among various types of innovation subjects, orderly flow of innovation factors, and sustainable optimization of the innovation ecosystem, so as to enhance the overall effectiveness of the innovation system.The State Council of the Central Committee of the Communist Party of China (CPC) issued the Overall Plan for Comprehensive Reform of Market-based Allocation of Factors in January 2022, emphasizing that for a significant period of time in the future, emphasis should be placed on the smooth flow of factors in a broader context.It can be seen that the orderly flow of innovation factors is very critical to regional innovation, and the smooth flow of technology factors, as the most central component of innovation factors, is crucial to regional innovation.
As the core region of China's science and technology development and productivity promotion, the Beijing-Tianjin-Hebei region is an essential part of the national development strategic plan, and its economic and scientific development has attracted much attention.The total quantity of innovation resources in Beijing, Tianjin and Hebei is abundant, but the allocation of science and technology innovation resources in the three regions is uneven and the mobility is low [2].According to statistics, the technology contracts flowing from Beijing to Tianjin and Hebei in 2021 were 5,434, with a turnover of 35.04 billion yuan, accounting for only 8.1% of all technology contracts flowing from Beijing to other provinces and cities, with more than 90% flowing to regions outside of Tianjin and Hebei, especially the Yangtze River Delta(YRD), Guangdong-Hong Kong-Macao Greater Bay Area(GBA), etc.It is evident that the migration of innovation achievements from Beijing to the Beijing-Tianjin-Hebei region is obviously insufficient.In this context, how to promote the flow of innovation factors in the Beijing-Tianjin-Hebei region and play an essential role in promoting regional innovation has become a new issue that needs to be urgently explored.
So far, limited attention has been devoted to the knowledge flow network in the Beijing-Tianjin-Hebei region.From the perspective of patent transfer, it has mostly focused on the characteristics of technology transfer in terms of subjects and objects (Zhang et al., 2017) [3], technology transfer policies (Wang, 2020) [4], and technology transfer network governance (Shi, 2015) [5], but the granularity of the related network research is not fine enough.And the phenomenon of innovation subjects embedded in mobility networks of various geographical scopes and spatial scales has been neglected to some extent.In this paper, we obtain data on invention patent assignments in the Beijing-Tianjin-Hebei region for the period 2003-2021, which enables us to study the characteristics of the intra-city(district) and inter-city(district) invention patent flows in the Beijing-Tianjin-Hebei region.What are the most active types of organizations in patent assignment?Are they enterprises, colleges & universities, or scientific institutions?Which innovation agents and cities (districts) dominate the flow of technology based on the transfer of invention patents?In order to answer these questions, we categorize the innovative subjects involved in patent transfer into two parts: transferor and transferee.In addition, combined with the address information of innovation subjects, we are able to further track the flow of patented technologies at different spatial scales with the help of social network analysis methods.Based on the above background, this paper concentrates on three aspects: (1) the characteristics of patent technology flow in Beijing-Tianjin-Hebei region.(2) the construction of multi-level patent technology flow network that encompasses the overall, intracity (district), and inter-city (district).(3) the dynamic evolution of multi-level patent technology flow network.
The remaining amount of the paper appears as follows.Section 2 examines the literature on regional innovation network, technology mobility.Section 3 presents the research design, data sources and network construction.Section 4 analyzes the characteristics of patent technology flows in the Beijing-Tianjin-Hebei region.Section 5 examines the dynamic evolution of the multi-level patent technology flow network in the Beijing-Tianjin-Hebei region.Section 6 summarizes the main research findings and sets forward countermeasure suggestions.

Regional innovation network
The study of regional innovation networks began with the introduction of the concept of innovation networks (Freeman, 1991) [6].An innovation network is a network structure in which firms, governments, academic and research institutions interact with each other within a certain region and establish interconnections through the selection of partners [7].Regional innovation networks are based on the interaction of subjects and form stable systems through adaptive behavior, revealing the law of knotting in the development of regional innovation systems [8][9][10].
In order to scientifically explore regional innovation in the era of network society, regional innovation network research has been initiated in economic geography.The accumulation and acquisition of relational data is a key link in the construction and quantitative analysis of regional innovation networks [11].At present, there are two primary approaches.One is to measure the strength of inter-regional innovation linkages using a modified gravity model [12].The second is to construct inter-regional knowledge flow or collaborative innovation networks based on data such as patent citations and paper collaboration [13,14].
On this basis, network structure, evolutionary trajectories, and spatial scales of knowledge spillover have become the focal point of regional innovation network research.For example, Hoekman et al. (2010) [15] explored the impact of spatial distance and geographical boundaries on regional innovation networks using data from 313 regional cooperation papers in 33 European countries from 2000-2017.Ye et al. (2015) [16] used the patent statistics database of the United States Patent and Trademark Office (USPTO) as the basis, and used methods such as k-core and block modeling in social network analysis to construct transnational patent citation networks in the field of electrical and electronic technology in three different periods from , and analyzed the patterns and characteristics of international knowledge flows.Li and Phelps (2017) [17] analyzed the polycentric characteristics and dynamic evolution of knowledge networks in the Yangtze River Delta urban agglomeration at various spatial scales based on the data of collaborative papers from WOS from 2000-2014.Liu et al. (2022) [18] constructed a global knowledge flow network based on the 2002-2016 United States Patent and Trademark Office (USPTO) dataset by combining patent transfer analysis with social network analysis to study global knowledge flow from the perspective of patent transfer, and found that an increasing number of inventors and assignees participated in the global knowledge flow network, with China and India rapidly rising in the list of knowledge creators and users, with the U.S. being the largest net knowledge inflow participant and the U.K. being the largest net knowledge outflow participant, and the small-world effect is increasingly evident in the cross-border knowledge flow network consisting of 35 major players.

Technology flow
Various actors in the regional network are able to realize continuous innovation through the flow of innovative factors such as technology, which in turn enhances regional innovation capacity [19].Technology flow is a highly abstract generalization of the concepts of technology transfer, technology diffusion, technology introduction, etc.It is a complex process involving many factors such as technology, economy, society, enterprises, information and humanities, based on the participants of the flow behavior, supported by the socio-economic and cultural environment, powered by the technology potential difference, and conditioned by the flow of information and materials [20].
Patent data are extensively used to measure technology flows [21][22][23].Because patent data contain a large quantity of useful information, have a long time span and relatively complete and stable data sources, they can better characterize knowledge production, technological change and regional economic development [24][25][26].Many existing studies on technology transfers are mostly based on the analysis of patent citations [27][28][29], patent licensing [30,31].In this paper, we divide and arrange them accordingly based on the research level.1. Regional level.Jeon and Lee (2014) [32] examined the flow of virtualization technologies between various countries (regions) based on patent citation data.on the other hand, Andersen (2017) [33] chose patent cooperation data as an indicator of technology transfers, and analyzed the impact of regional trade agreements on patent cooperation across countries.Gae ´tan and Florian (2020) [34] investigated the sources of knowledge flows between developed and developing countries using patent data and found that North America is more likely to benefit from reverse knowledge flows than Europe as China emerges as a technology leader.[38] used company patent matching data from Japanese manufacturing multinationals to examine the feasibility of allocating more R&D activities allocation to country-industries with greater intensity of knowledge flows would improve innovation performance of MNCs.
3. Technology level.Lai et al. (2007) [39] measured the technology flow among seven industries including computer hardware, computer software, communication finance, and ecommerce.Chu and Su (2015) [40] understood the knowledge flow among different types of knowledge owners as assignees of patented technology by identifying the inventor location of the first assignee type.Jiang et al. (2019) [41] used patent citations as indicator of knowledge flow, examined the impact of firms' global patent social networks on the knowledge flow of business method software patents and found that firms in a relatively central position or located within the same structural equivalent cluster had more citations to their counterparts' patents, and that knowledge transfer was positively facilitated when both the citing and cited firms performed the roles of rover and gatekeeper/representative, while the gatekeeper/representative companies (alone) cite fewer patents from companies that do not perform such roles.Giglio et al. (2021) [42] propose a method to study cross-country creativity/knowledge flows by analyzing patent citation networks using the aircraft, aviation and aerospace (AAC) industry as a case study.Smojver et al. (2021) [43] identify technology life cycle by performing a dynamic analysis of patent citation networks to stages, mapping patent co-citation networks from patent citation networks, and applying link prediction algorithms to patent co-citation networks to explore knowledge flows within technology domains.

Current research status
In recent years, domestic and foreign economic geographers have conducted in-depth research on regional innovation networks and achieved a series of valuable research results.However, research cases mostly focus on innovation networks led by multinational corporations in developed countries, while research on innovation networks led by local enterprises in developing countries and regions lacks attention.There are numerous studies on intra-city(district) or inter-city(district) innovation networks at a single spatial scale, but there is insufficient research on the evolution laws of innovation networks at multiple spatial scales.We argue that based on different spatial couplings, analyzing the evolutionary process and mechanism of the innovation network, and systematically portraying the pattern and structure of the innovation network from the perspective of time-space topology should be emphasized.
For research on technology flow, scholars at home and abroad have mostly focused on the cooperative R&D perspective.However, the purpose of cooperative R&D is to reduce the difficulty of technical knowledge production rather than to enhance the value of knowledge, and in fact, most of the patents cannot be transformed and applied in the end.In addition, the cooperative R&D of patented technology does not clarify the specific flow trajectory of knowledge among innovation subjects, which makes the innovation network based on patented technology not have directional characteristics.We argue that both cooperative R&D and transfer of patented technology are a form of innovative knowledge flow, but they are in two stages of the innovation chain respectively.The former belongs to the knowledge production stage and the latter belongs to the knowledge application stage.The transfer of patented technology has obvious directional characteristics, while only technical knowledge with application value can be accepted by the transferee of patented technology.Therefore, a re-examination of the structural characteristics and evolutionary patterns of regional innovation networks from the perspective of patent transfers can be attempted in the future.

Research design
The research object of this paper is 43 cities (districts) in the Beijing-Tianjin-Hebei region, each of which is treated as a separate region.The research framework of this paper is shown in Fig 1 .Firstly, the data of invention patent transfer in 43 cities (districts) in the Beijing-Tianjin-Hebei region with all the transfer (transferee) organization addresses are collected, and the transfer execution year is set as the time node.Then, the characteristics of technology flow in the Beijing-Tianjin-Hebei region are analyzed in three aspects of flow quantity change, flow subject type and spatial distribution characteristics, and a multi-level patent technology flow network in the Beijing-Tianjin-Hebei region is constructed.Finally, the structural characteristics and node characteristics of each level of network are investigated separately.

Data sources
The invention patent data used in this paper comes from the State Intellectual Property Office of China, on the basis of which we utilize the Qizhidao (https://patents.qizhidao.com/)and Qichacha (https://www.qcc.com/)data platform for searching, cleaning, processing and other work of patent data, the specific steps are as follows.First of all, Searching for transferred patents (only invention patents are considered) from the search service of the patent database of Qizhidao (https://patents.qizhidao.com/),each patent transfer data includes information such as application number, public number, title, application date, announcement date, transferor, transferee, transfer execution date, and number of transfers.Then, relying on the enterprise data platform Qichacha (https://www.qcc.com/), the address information of the transferor (transferee) is searched and identified one by one to ensure that the transferor (transferee) is located in the cities (districts) of Beijing, Tianjin and Hebei.After searching and downloading the patent data, we finally obtained 47,572 invention patent assignments within the Beijing-Tianjin-Hebei region from 2003 to 2021, excluding 47,084 invention patent assignments in which both parties of the assignee and transferee were individuals, involving 15,672 organizations.

Network construction
The fundamental model of multi-level patent technology flow network is shown in Fig 2 .Assuming that there are four transferred invention patents P1, P2, P3 and P4, the organizations concerned are six, O1, O2, O3, O4, O5 and O6, among which four enterprises, one college and university and one scientific institution are distributed in region R1, region R2 and region R3.The transfer relationships among the organizations involved can be expressed as six pairs of network relationships, which are O2!O1, O2!O3, O3!O4, O4!O3, O4!O5, O6!O5.
The transfer relationship between organizations crosses city (district) boundaries and establishes a multi-level patent technology flow network, which is dismantled to include intra-city (district) patent technology flow network and inter-city (district) patent technology flow network.When the assignor and the assignee of a patent for invention are located in the same city (district), such as O2!O1, the intra-city (district) patent technology flow relationship is formed.When the assignor and assignee of a patent for an invention are located in distinct cities (districts), such as O6!O5, the inter-city (district) patent technology flow relationship is formed.The intra-city (district) patent technology flow network is a network formed by the transfer of invention patents between organizations in the same city (district), when the nodes of the network are organizations located in the city (district), and the edge is the patent transfer relationship between organizations in the city (district).The inter-city (district) patent technology flow network consists of the transfer relationship between organizations across regional boundaries, at which time the network node is a city (district), and the edge is the transfer relationship of invention patents formed between cities (districts).
This paper employs the date of execution of invention patent assignment to determine the time when the network nodes establish relationships.This paper assesses the patent technology flow network based on three levels of invention patent assignment:  2. From 2011 to 2014, however, the number of patent flows significantly increased and displayed a large fluctuation trend, primarily because of The "Capital Economic Circle" concept, which was first introduced in the outline of the 12th Five-Year Plan in 2011 and encourages the integrated development of Beijing, Tianjin, and Hebei, may be the primary factor.The decline in patent technology flow in 2012 and 2014 may also be related to the chaos caused by patent infringement and counterfeiting during these two years.
3. The number of patent technology flows in the Beijing-Tianjin-Hebei region show a consistent rise between 2015 and 2020, which may be directly tied to the State Council's decision in February 2014 to elevate the cooperative development of Beijing-Tianjin-Hebei to the status of a major national plan.
4. Since 2021 is the first year of the 14th Five-Year Plan period, there will be an increase in the number of patent technology flows in Beijing-Tianjin-Hebei, reaching more than twice the number of patent technology flows in 2020.Beijing, Tianjin, and Hebei released the "14th Five-Year Plan for Intellectual Property Development" in the first year of the 14th Five-Year Plan period, proposing to enhance the mechanism of collaborative development and promote suitable intellectual property flows, among other things.
Based on the transfer (transferee) organization's geographic and spatial situation, the intra-city (district) and inter-city (district) technology flows are differentiated.Fig 4 demonstrates that, with the exception of 2003, the patent technology flow in the Beijing-Tianjin-Hebei region was mostly carried out within cities (districts) prior to 2012.However, with the concepts of "Capital Economic Circle," "Beijing-Tianjin-Hebei Integrated Development," and "Beijing-Tianjin-Hebei Cooperative Development," the technology flow across administrative boundaries began.However, overall, in the Beijing-Tianjin-Hebei region, the intra-city (district) technology flow is greater than the inter-city (district) technology flow.

Spatial distribution characteristics
In this paper, the 43 cities (districts) in Beijing-Tianjin-Hebei are divided into four types, i.e., HH-type of "high outflow and high inflow", HL-type of "high outflow and low inflow", LHtype with "low outflow and high inflow", and LL-type with "low outflow and low inflow" using the average value of the inflow and outflow of patented technology in each city (district) as the boundary, as shown in Fig 6(a), where the horizontal axis represents outflow and the vertical axis represents inflow.Since the distribution of cities (districts) in the LL-type is relatively dense, it is difficult to see the specific cities (districts), so the other parts of There are significant differences in the number of patented technology flows among cities (districts) in the Beijing-Tianjin-Hebei region.The flow of patented technology is mainly concentrated in the central urban areas of Beijing, such as BHD (Haidian District),BCY (Chaoyang District) and BDX(Daxing District), while only HSJZ(Shijiazhuang) and TBHXQ(Binhai New Area) in Hebei and Tianjin have more frequent flows, showing a more obvious characteristic of "more in the central city and less in the peripheral cities".Specifically, the HH-type contains BCP (Changping District), BCY (Chaoyang District), BDX (Daxing District), BFT (Fengtai District), BHD (Haidian District), BXC (Xicheng District), TBHXQ (Binhai New Area), HSJZ (Shijiazhuang) eight cities (districts), which are more active in innovation and have stronger innovation capacity, and can realize continuous innovation through intraor cross-regional technology flows.The LH-type contains two cities (districts), BHR (Huairou District) and BSY (Shunyi District), which are good at absorbing external knowledge, but their external spillover capacity needs to be improved.The remaining 33 cities (districts) belong to the LL-type, which have a low number of patented technology flows, lack of interaction between the region and the outside, and insufficient knowledge flows and spillovers.

Structural features.
The patent technology flow network in Beijing-Tianjin-Hebei region consists of knowledge flows among organizations located in 43 cities (districts).In this paper, the network size, network density, average clustering coefficient and network transmission coefficient of the overall patent technology flow network in Beijing-Tianjin-Hebei region from 2004 to 2021 and in each period were measured using Ucinet software (Table 1) to reflect the structural characteristics of the overall patent technology flow network and its temporal changes.
The whole patent technology flow network in the Beijing-Tianjin-Hebei region has 627 nodes in 2004-2009, 4057 network nodes in 2010-2015, and 12752 network nodes in 2015-2021.In the process of the patent technology flow network going through three periods, many new flow subjects enter the network, and the network scale increases significantly.In terms of the network density of the patent technology flow network, with the expansion of the network scale, a large number of new flow subjects enter the network, and the network density gradually decreases, forming an increasingly loose and sparse network.As a whole, the patent technology flow network in Beijing-Tianjin-Hebei region has been in a low-density network state during the study period.
The average clustering coefficient increases significantly from the first to the third period, especially during the evolution from the first period (2004-2009) to the second period (2010-2015), the average clustering coefficient changes by a larger magnitude, and some of the network nodes become closer to each other, with a significant increase in the trend of smallgroup technology mobility.In contrast, the evolution from the second period (2010-2015) to the third period (2016-2021) is characterized by a smaller change in the average clustering coefficient and a slowdown in the growth of concentration among some network nodes.Although the size of the network is more than three times larger than the size of the network in the second period, fewer mobile subjects newly entering the network in the latter period are involved in the centralized network.As can be seen from Table 1, the network transmission coefficient gradually decreases from the first period to the third period, indicating that with the entry of a large number of new flow subjects, the existing nodes are more inclined to establish transferring relationships with the newly entered mobile subjects.
After measuring and analyzing the stage-by-stage structural characteristics of the overall patent technology flow network in the Beijing-Tianjin-Hebei region, this paper uses the Gephi 0.9.7 software to visualize the patent technology flow network, showing the patent technology flow network in the three periods of [2004][2005][2006][2007][2008][2009][2010][2011][2012][2013][2014][2015], and 2016-2021, as respectively shown in Figs 7-9.Where the organizations are the nodes of the patent technology flow network, the size of the node circle represents the number of other organizations that directly transferor (transferee) technology with the node, i.e., the node degree, the number on the node represents the organization's ID number in the study of this paper, and the line is the technology transfer relationship between organizations, and its thickness represents the number of times of technology transfers between organizations.
The main organizational nodes of the patent technology flow network in Beijing-Tianjin-Hebei region from 2004 to 2009 are Organization 6551 (Tianshili Pharmaceutical Group Co., Ltd.), Organization 5166 (Tsinghua University), Organization 8189 (China Banknote Printing and Minting Group Co., Ltd.), Organization 410 (Peking University), Organization 1570(Beijing Qin Tian Science & Technology Group Co., Ltd.), Organization 1915(Beijing SiFang Automation Co., Ltd.), Organization 1916(Beijing Sifang Rugang Concrete Products Co., Ltd), Organization 6909 (Wei Ming Bio-Agricultural Group Co., Ltd.), Organization 2374 (Increasepharm), Organization 3143(Feijiu Medical Technology (Beijing) Co., Ltd), etc.They have the highest number of transfer (transferee) relationships with other nodes and are among the top ten nodes in terms of node degree in the network of flow of patented technologies (Fig 7).In 2004-2009, there were more flows within the Beijing-Tianjin-Hebei region's patent  Unlike the previous period, the number of colleges and universities among the major nodes with node degrees in the top ten has risen, from two in the previous period to six in this period, while the number of patented technology transfers has also increased significantly.Compared to the previous two periods, the number of colleges and universities in the top ten major nodes in terms of node degree has risen further, from six in the previous period to nine in this period, and the node degree of each node significantly increases.It shows that over time, the colleges and universities as the main producers of scientific and technological achievements, have gradually increased their participation in the Beijing-Tianjin-Hebei region's patent technology flow network.
5.1.2Node characteristics.This paper uses Ucinet software to measure the weighted centrality, closeness centrality, and betweenness centrality of the nodes in the overall patented technology flow network in the Beijing-Tianjin-Hebei region from 2004 to 2021, and lists the organizations of the nodes that are ranked among the top ten in terms of the weighted outdegree centrality of the overall patented technology flow network during the three periods and their closeness centrality, and betweenness centrality respectively, as shown in Table 2.As a whole, the mean value of weighted centrality has been increasing over the three periods, and closeness centrality has continued to decrease.It suggests that organizations are participating in the flow of patented technologies more and more frequently over time, but that the interconnectedness of the organizations is weakening as the size of the network continues to grow.The top ten organizations in terms of weighted out-degree centrality have constantly changed across the periods, but Tsinghua University has been consistently ranked among them.Its mediated centrality has continued to rise, from 0.001 in the first period to 0.007 in the second period to 0.012 in the third period.It can be seen that Tsinghua University occupies a very important position in the Beijing-Tianjin-Hebei patented technology flow network and has a strong control over the flow of patented technology.
In order to clarify the roles played by different types of organizations in the overall patent technology flow network in the Beijing-Tianjin-Hebei region and the roles they play, this paper divides the types of organizations into six categories: enterprises, individuals, colleges & universities, agency groups, scientific institutions, and others, and analyzes the node characteristics of different types of organizations respectively.Table 3 is produced after categorizing and quantifying the weighted centrality, closeness centrality, and betweenness centrality of each type of organization node.Enterprises are the organizational types with the highest weighted centrality, closeness centrality, and betweenness centrality over the course of different time periods, while differences in centrality for other organizational types are less pronounced.This suggests that enterprises serve as the primary hubs of the patent technology flow network in the Beijing-Tianjin-Hebei region.Individual invention patent technology transfer also occupies a high proportion in the Beijing-Tianjin-Hebei region, mainly in the form of individual invention patents owned by enterprises.The amount of technical flows coming from colleges & universities has significantly increased, and their the out-closeness centrality is higher than in-closeness centrality, while the betweenness centrality is lower in comparison.This shows that colleges & universities have some radiation ability to other organization types in the patent technology flow network in the Beijing-Tianjin-Hebei region, but they do not currently play the role of "bridge."Even though agency groups and scientific institutions have fewer technology flows, their in-closeness centrality and betweenness centrality are better, indicating that they have some resource integration power in the Beijing-Tianjin-Hebei region's patent technology flow network.Indicating that the patent technology flow in the Beijing-Tianjin-Hebei region is gradually active and no longer heavily relies on a single type of organization for patent technology transfer, the gap of intermediary centrality among the organization types gradually narrows over time.

Dynamic evolution of the intra-city (district) patent technology flow network
When analyzing the network of patented technology flows of the intra-city (district), due to the large number of cities (districts) and limited space, some cities (districts) have smaller network sizes and simpler relationships between nodes.Therefore, this section only lists some cities (districts) as sample objects to describe the network of patented technology flows within their cities (districts).The majority of issued invention patents and intra-city (district) patent technology flow in the Beijing-Tianjin-Hebei region are produced in eight cities (districts), including BHD(Haidian District), BCY(Chaoyang District), HSJZ(Shijiazhuang), TBHXQ (Binhai New Area), BDX(Daxing District), BXC(Xicheng District), BCP(Changping District), and HBD(Baoding).Therefore, this paper firstly measures the structural characteristics of intra-city (district) patent technology flow network in eight cities (districts), and the specific results are shown in Table 4. On this basis, three cities (districts), namely, BHD, HSJZ and TBHXQ, are selected as the key cities (districts) to visualize and analyze their intra-city (district) patent technology flow network.

Structural features.
1. 2004-2009.The structural characteristics of the intra-city (district) patent technology flow networks of the eight chosen cities (districts) varied noticeably between 2004 and 2009.The intra-city (district) patent technology flow network has 160 nodes in BHD, 25 in BCY and BDX, and less than 20 in the other five cities (districts).There are obvious differences in network size between the cities (districts), with BHD being about eight times larger than most cities (districts).Among the eight cities (districts), HBD's intra-city (district) patent technology flow network is the smallest.Despite having the greatest intra-city (district) patent technology flow network, BHD's network density is the lowest when compared to the other seven cities (districts).In general, cities (districts) with lower network size have relatively high network densities at this time.Numerous mobile subjects joined the network as a result of the network's gradual development in size, but because they did not establish stronger connections, the network's density gradually shrank.At this point, although the network sizes of BCY and HSJZ are the same, the network density of HSJZ is slightly higher than that of BCY, which shows that HSJZ is more closely connected among mobile subjects.
The average clustering coefficient is used to gauge how closely connected the nodes in the patent technology flow network are to one another.The mobile subjects in these cities (districts) did not realize mutual connection in the intra-city (district) patent technology flow network during this period, and they had not yet formed the trend of small group technology flow, as evidenced by the average clustering coefficients of all eight cities (districts) during this period being 0. The network transmission coefficient shows whether there is a chance for transfer relationships to form between mobile subjects in the network and the transferee(transferor) of the transferor (transferee).The fact that none of the eight cities (districts) have any network transmission coefficients during this time period suggests that mobile subjects there are more likely to seek out new mobile subjects from outside the network for the transfer of patent technology than they are to establish transfer relations with the transferee(transferor) of the transferor (transferee).Although there is a big variety in network scale between cities (districts), BXC has the highest network density and the closest connections between moving subjects.HSJZ, TBHXQ, and BDX's average clustering coefficients have decreased, and the trend of small group technology flow has not improved.Except for BCY, BXC, and HBD, the network transmission coefficients of the other five cities (districts) have decreased.
In order to more clearly portray the intra-city (district) patent technology flow network of key cities (districts), this paper uses Gephi 0.  lists the top ten node organizations in the intra-city (district) patent technology flow network of the three key cities (districts) in terms of weighted out-degree centrality, as well as their closeness centrality and betweenness centrality, the details of which are shown in Table 5.
In the intra-city (district) patent technology flow network in BHD, the weighted centrality of the top 10 important node organizations in terms of weighted out-degree centrality has obvious differences, but the differences in closeness centrality and betweenness centrality are smaller.Among them, Tsinghua University and Beihang University perform more prominently, while the betweenness centrality of more nodal organizations is 0. It can be seen that the nodal organizations with higher weighted out-degree centrality are more likely to form patent technology transfer pairs and do not realize a larger influence range and stronger ability to connect other nodes in the network.The differences in weighted centrality, closeness centrality, and betweenness centrality of the top 10 important node organizations in the intra-city (district) patent technology flow network in HSJZ are smaller than those in BHD.Although the weighted out-degree centrality of Hebei University of Science and Technology is smaller than that of Shiba Pharmaceutical Group Zhongqi Pharmaceutical Technology (Shijiazhuang) Company Limited, it's closeness centrality and betweenness centrality are significantly higher than those of the latter.It can be seen that Hebei University of Science and Technology occupies a very important position in the intra-city (district) patent technology flow network of HSJZ, and has a certain degree of resource integration, radiation, and control ability.For TBHXQ, the 18th Research Institute of China Electronics Technology Group Corporation has the best weighted out-degree centrality performance, which is located in the first place of each node organization, and Tianjin University of Science & Technology has the best out-closeness centrality and betweenness centrality performance.Table 6 shows the weighted centrality, closeness centrality, and betweenness centrality of nodes of different organization types in eight cities (districts).In contrast, the weighted centrality of enterprises is significantly higher, while individuals, colleges and universities, scientific institutions, agency groups, and others are relatively smaller.The betweenness centrality of enterprises in TBHXQ, BDX, BXC, and BCP is higher than that of other cities (districts), which means that enterprises have more influence in the intra-city (district) patent technology flow network of these four cities (districts) and give full play to the role of "bridge."Although the weighted centrality of individuals in BCY is lower than that of enterprises, its betweenness centrality is significantly higher than that of other organization types, indicating that individuals have a certain resource integration ability and control in the intra-city (district) patent technology flow network in BCY.The betweenness centrality of each organization type in BHD and HSJZ is smaller and less concentrated than that of other cities (districts), indicating that the intra-city (district) patent technology flow network of these two cities (districts) is more active in each organization type and does not rely excessively on a single type of organization for patent technology transfer.For HBD, although the weighted centrality of colleges and universities is smaller compared with that of enterprises, the out-closeness centrality and betweenness centrality perform better, which shows that colleges and universities have certain radiation power and resource integration power in the intra-city (district) patent technology flow network of HBD.

Structural features.
After portraying the overall patent technology flow network in the Beijing-Tianjin-Hebei region and the intra-city (district) patent technology flow network of each city (district), this subsection constructs the inter-city (district) patent technology flow network in the Beijing-Tianjin-Hebei region with each city (district) as the node and measures the relevant network indicators to reflect the structural characteristics of the inter-city (district) patent technology flow network, which are shown in Table 7.The network consists of 43 cities (districts) in the Beijing-Tianjin-Hebei region as nodes and their inter-city (district) patent technology transfer relationships.On the whole, the size of the inter-city (district) patent technology flow network in the Beijing-Tianjin-Hebei region has been expanding, and all 43 cities (districts) participate in the network.The network density, the average clustering coefficient, and the network transmission coefficient increase significantly.The patent technology flow between cities (districts) is gradually active, and the trend of small group technology flow is obvious.
This section uses Gephi 0.9.7 software to map the patent technology flow network between cities (districts) in the Beijing-Tianjin-Hebei region in different periods, 2004-2009, 2010-2015, 2016-2021 and 2004-2021, to reflect more clearly the dynamic evolution of the patent technology flow network between cities (districts) in Beijing-Tianjin-Hebei region, as shown     (district) patent technology flow network in the Beijing-Tianjin-Hebei region shows specific preferences.Each city (district) prefers to conduct patent technology transfer with its own province (city) or neighboring cities (districts).Geographical proximity has a greater influence on the network structure of the inter-city (district) patent technology flow network in the Beijing-Tianjin-Hebei region.In terms of the color of nodes, the clustering situation in this period has changed somewhat compared with the previous period.However, on the whole, cities (districts) still tend to transfer patent technology with their own province (city) or neighboring cities (districts).
3. 2016-2021.In the period of 2016-2021, the size of the inter-city (district) patent technology flow network has included all the cities (districts) in the Beijing-Tianjin-Hebei region, and more patent technology transfer relationships have been generated in the network, as shown in Fig 15 .The network density becomes 0.487 265, which is a more obvious increase compared with the previous two periods.It implies a significant increase in the number of organizations and relationships involved in cross-regional patent technology transfer.The average clustering coefficient and network transmission coefficient have also increased to a certain extent.BHD has been in the most central position in the inter-city (district) patent technology flow network in the Beijing-Tianjin-Hebei region.The gap between the size of nodes in the network of TBHXQ, BDX, BCY, BCP, BXC, HSJZ, and other cities (districts) and BHD is gradually narrowing, and the influence in the network is gradually increasing.In terms of the color of the nodes, the clustering situation in this period has increased the cohesion among cities (districts) compared with the previous period.Patent technology transfer in this period is mainly influenced by the geographical distance between cities (districts).
The characteristics of the inter-city (district) patent technology flow network in the Beijing-Tianjin-Hebei region for the whole period from 2004 to 2021 remain consistent with those of the 2016-2021 period.All 43 cities (districts) participate in the inter-city (district) patent technology flow network for the whole period.The network density, average clustering coefficient, and network transmission coefficient do not differ significantly compared with those of 2016-2021.BHD is always the most frequent region in the Beijing-Tianjin-Hebei region in terms of patent technology flow with other cities (districts).

Node characteristics.
In this paper, on the basis of drawing the inter-city (district) patent technology flow network in the Beijing-Tianjin-Hebei region, the position of each city (district) in the inter-city (district) patent technology flow network is determined by calculating the characteristic indicators of weighted centrality, closeness centrality, and betweenness centrality of each city (district), and the results are shown in Table 8, which are analyzed as follows.
1.In terms of weighted centrality, the weighted centrality of BHD has remained stable at the top in all periods.The weighted out-degree centrality is significantly higher than the weighted in-degree centrality, indicating the absolute central position and influence of BHD in the inter-city (district) patent technology flow network in the Beijing-Tianjin-Hebei region.BHD has a strong influence on the flow of patented technology to other cities (districts), and is able to obtain considerable benefits from the flow of patented technology from other cities (districts).The weighted centrality of BXC has increased during 2010-2015 and is in the second place among 43 cities (districts), mainly due to the frequent patent technology flow between the research units and subsidiaries of State Grid Corporation.Specifically, for each city in Hebei Province, the weighted in-degree centrality is significantly higher than the weighted out-degree centrality for all 10 cities except HQHD during 2016-2021.It indicates that there is a certain innovation gap among cities in Hebei Province, and central cities such as HSJZ and HBD have limited patent technology flow to other cities, and more advanced technological innovation results are obtained from some regions in Beijing and Tianjin.For Tianjin, the phenomenon of polarization of patent technology flow in each district is serious.With significant differences, TBHXQ has been in the forefront at all stages, while TNH and TJZ have been at the bottom of the cities (districts) in Beijing-Tianjin-Hebei region.
2. In terms of closeness centrality, the closeness centrality of each city (district) from 2016 to 2021 has increased significantly compared with the previous two periods, which means that each city (district) has improved both in terms of integration and radiation, and the intercity (district) patent technology flow network in the Beijing-Tianjin-Hebei region has formed a better foundation and has certain long-term development momentum.BHD, TBHXQ, and BDX have the highest in-closeness and out-closeness centrality, and the outcloseness centrality is greater than the in-closeness centrality, which means that these three regions have stronger radiation ability to other cities (districts) in the inter-city (district) patent technology flow network in the Beijing-Tianjin-Hebei region.HTS's in-closeness centrality leaped from 2016 to 2021, ranking 3rd among 43 cities (districts), thanks to its active connection to Beijing-Tianjin innovation sources in recent years, and its efforts to integrate innovation resources and promote the transfer and transformation of scientific and technological achievements.Lower out-closeness centrality, such as TNH, TJZ, BMY, and BYQ, these areas have more scarce innovation resources, innovation achievements, sparse innovation relationships, and lower technology flow benefits.
3. In terms of betweenness centrality, the betweenness centrality of each city (district) fluctuated greatly in these three stages.The betweenness centrality of cities (districts) with high weighted centrality or closeness centrality, represented by BHD, BCY, and TBHXQ, has shown a continuous downward trend during the study period, and the gap between their betweenness centrality and that of other cities (districts) has gradually narrowed.It indicates that over time, the 43 cities (districts) in the Beijing-Tianjin-Hebei region have gradually become more active in the flow of patented technologies, and are no longer overly dependent on a particular city (district) for the transfer of patented technologies.In addition, the betweenness centrality of HTS, TBC, and TDL gradually increased during the study period and ranked among the top 10 cities (districts) in the 43 cities (districts) from  and research institutes to carry out key technology and common technology research and development according to the actual technology needs of Tianjin and Hebei, on the basis of which Tianjin and Hebei will transform and reinvent key technology and common technology to improve their own innovation level.On the other hand, promote Beijing, Tianjin, and Hebei to jointly build a technology cooperation R&D platform, explore the establishment of innovation resources and innovation revenue sharing mechanism, improve the intellectual property protection system, and help the reasonable flow of technology elements in Beijing, Tianjin, and Hebei.
3. The regulations on patent technology transfer in each city (district) should be improved, and an effective institutional mechanism and incentive mechanism should be established, so as to actively encourage and guide the innovation main bodies within the region to establish cross-regional patent technology transfer relations and obtain more heterogeneous knowledge, while at the same time, optimizing the technological innovation environment within the region, promoting the flow and diffusion of such heterogeneous knowledge in the region, and enhancing the performance of regional innovation.
Although this paper employs a social network analysis approach to provide some valuable insights into the spatio-temporal evolution of technology flows in the Beijing-Tianjin-Hebei region of China, it also has some limitations.For example, the use of invention patent transfer data to construct intra-city (district) and inter-city (district) patent technology flow networks at the city (district) level as a reflection of formal technology flow relationships may ignore the informal technology flow processes among innovation agents.Therefore, the understanding and knowledge of the composition and structural features in the informal technology flow network can be further deepened in the future.

4 . 1
(1) the overall patent technology flow network composed of assignment relationships among all flow subjects.(2) the intra-city (district) patent technology flow network composed of assignment relationships among flow subjects located in the same city (district).(3) the inter-city (district) patent technology flow network composed of assignment relationships among flow subjects spanning different cities (districts), with 43 cities (districts) in Beijing, Tianjin and Hebei, including 16 municipal districts in Beijing, 16 municipal districts in Tianjin and 11 municipalities in Hebei as network nodes, and the transfer relationship between cities (districts) as inter-node links.4 Characteristics of the Beijing-Tianjin-Hebei region's patent technology flow Quantity change In the Beijing-Tianjin-Hebei region, there were 47,084 patent technology flows between 2003 and 2021.The number of patent technology flows grows together with the overall number of
In order to more clearly reflect the dynamic characteristics of the patent technology flow network in the Beijing-Tianjin-Hebei region from 2003 to 2021, this paper divides the research time length into three periods: 2003-2009, 2010-2015, and 2016-2021.Among them, the network scale in 2003 is smaller, involving only four nodes.At the same time, to ensure the same time length in each period, this paper rounds off 2003 and adjusts the research time length to 2004-2009, 2010-2015, 2016-2021.

2 .
[2010][2011][2012][2013][2014][2015].The intra-city (district) patent technology flow network of each city (district) underwent more significant change between 2010 and 2015 compared to the first period.More flow subjects joined the patent technology flow network of each city (district), and the network's size increased exponentially or by a factor of several.With 730 organizations becoming nodes of the intra-city (district) patent technology flow network, BHD continues to be the city (district) in the Beijing-Tianjin-Hebei region with the largest intra-city (district) patent technology flow network.HSJZ's network size achieved a large jump with 185 nodes, surpassing BCY and ranking second among the eight cities (districts).Compared to the previous period, while the network size of the eight cities (districts) increased significantly, the network density decreased in all of them during this period.Except for BCY, BXC, and HBD, the average clustering coefficients and network transmission coefficients of the other five cities (districts) have increased.This indicates that the flow subjects in the network are more inclined to establish transferring relationships with the transferee(transferor) of the transferor (transferee), and that the tendency of the small-group technology flow has increased.3. 2016-2021.The intra-city (district) patent technology flow network of the eight cities (districts) is still undergoing substantial changes as the period 2016-2021 approaches.From the second period of 2010-2015 to the third period of 2016-2021, the network's size dramatically increases, and an increasing number of flow subjects join the intra-city (district) patent technology flow network.BHD and BXC are the cities (districts) with the biggest and smallest network scales, respectively.The intra-city (district) patent technology flow network includes 1,755 flow subjects participating in BHD, compared to just 147 in BXC.
9.7 software to visualize the intra-city (district) patent technology flow network, and shows the patent technology flow of BHD, HSJZ and TBHXQ from 2004-2009, 2010-2015, 2016-2021, and 2004-2021, as shown in Figs 10-12.Organizations like Organization 5166 (Tsinghua University), Organization 712 (Beihang University), and Organization 410 (Peking University) serve as core nodes in the intra-city (district) patent technology flow network in BHD.Other nodes have created numerous patent technology transfer pairs outside of the clusters these core nodes have created, but they haven't created a connectivity network.Several clusters with core nodes at Organization 3681 (Hebei University of Science and Technology) and Organization 3983 (North China Pharmaceutical Co., Ltd.) make up the intra-city (district) patent technology flow network in HSJZ.In the intra-city (district) patent technology flow network in HSJZ from 2010 to 2015, Organization 3983(North China Pharmaceutical Co., Ltd.) is the node with the most connections to other organizations when comparing different time periods.And from 2016 to 2021, Organization 3681(Hebei University of Science and Technology)'s patent technology transfer activities outpaced those of Organization 3983(North China Pharmaceutical Co., Ltd.), making it the node with the greatest number of connections to other businesses in the HSJZ intra-city (district) patent technology flow network.The Organization 6018 (Tianjin University of Science & Technology), Organization 6468 (Tianjin Yaoyu Biotechnology Co., Ltd.), and Organization 13963(Tiandy Digital Technology Co., Ltd.) are the most dominant nodal organizations in the intra-city (district) patent technology flow network of TBHXQ.The scope of their technology flow is significantly greater than that of other organizations, demonstrating their absolute central position and influence in the network.5.2.2 Node characteristics.This paper uses Ucinet software to measure the weighted centrality, closeness centrality, and betweenness centrality of each node in the intra-city (district) patent technology flow network of three key cities (districts), BHD, HSJZ, and TBHXQ, and

in Figs 13 - 16 .
Each city (district) is a node of the inter-city (district) patent technology flow network in the Beijing-Tianjin-Hebei region.The size of the node indicates the number of cities (districts) with which the node city (district) directly conducts patent technology transfer.The same color of nodes means they belong to the same cluster after clustering process.The

Table 7 . Structural characteristics of the inter-city (district) patent technology flow network in the Beijing-Tianjin-Hebei region.
https://doi.org/10.1371/journal.pone.0301509.t007 2. 2010-2015.With the concept of "Capital Economic Circle" put forward, the integrated development of Beijing, Tianjin and Hebei continues to advance.In the period of 2010-2015, the inter-city (district) patent technology flow network in the Beijing-Tianjin-Hebei region became more intensive compared with the previous period.The size of the network reached 43.Cities (districts) that did not join the patent technology flow network in the previous period began to establish links with other cities (districts).The network density in this period is 0.219 823, which is higher than that of the previous period.It can be seen from Fig 15 that the patent technology transfer relationship increased significantly at this time.The average clustering coefficient increased from 0.316 368 to 0.524 460, and the flow subjects in each city (district) began to show the trend of small group mobility and formed clusters.BHD is still the most influential node in the inter-city (district) patent technology flow network in the Beijing-Tianjin-Hebei region.Meanwhile, the influence of BXC has increased.During this period, BHD, BXC, BCY, BDX and other cities (districts) became nodes with frequent patent technology flow.